IPACS Electronic library

Is chaos a route to collapse ?

This paper deals with the dynamics of a single-degree-of-freedom unilateral damage oscillator. Using appropriate internal variables, the hysteretic dynamic system can be written as a non-smooth autonomous system. Free dynamics of such a non-linear system are simply reduced to periodic motion, eventually attractive trajectory and divergence motion. The natural frequency of this system depends on the stationary value of the damage internal variable. Nevertheless, the inelastic forced oscillator can exhibit very complex phenomena. When the damage parameter remains stationary, dynamics is similar to the one of an elastic oscillator with unsymmetrical stiffness. Dynamics appears to be controlled by the initial perturbations. Moreover, chaotic motions may appear in such a system, for severe damage values. Chaos can be understood as a route to collapse.